Replacing Points with objects
If the vertices are all one object, you could also use Dupliverts:


If the vertices are separate objects, join them with &#9096; CtrlJ
Parent the object to the vertices object.
Select the object you want to replace the vertices with and then the vertices object, then press &#9096; CtrlP> Object.


Enable Dupliverts in Properties > Object > Duplication on the vertices object:


If you want the duplicates to be on top of the vertices, make sure the object origins of both objects are in the same place. Use &#8679; ShiftS to snap the 3D cursor to an object and &#9096; Ctrl&#9095; Alt&#8679; ShiftC to snap the origin to the cursor.




Using dupliverts has the advantage that the object is instanced to each vertex, with in very efficient memory usage.

I just tested this by instancing a UV sphere to a > 20,000 vertex object with no trouble.